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Mathematics
Mathematics
Problem
If
x
=
tan
(
1
a
log
y
)
x = \tan \left( \frac{1}{a} \log y \right)
x
=
tan
(
a
1
lo
g
y
)
, then show that
(
1
+
x
2
)
d
2
y
d
x
2
=
(
a
−
2
x
)
d
y
d
x
(1+x^2) \frac{d^2 y}{dx^2} = (a-2x) \frac{dy}{dx}
(
1
+
x
2
)
d
x
2
d
2
y
=
(
a
−
2
x
)
d
x
d
y
.
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